What is the product of $\frac{1}{5}$ and $\frac{3}{7}$ ?
Explanation: A product is what you get when you multiply things together. To multiply fractions, multiply the numerators together to get the new numerator. So, the numerator is $1\times3=3$.

Then, multiply the denominators together to get the new denominator. $5\times7 = 35$. Therefore our answer is:  \[\frac{1}{5} \times \frac{3}{7} = \boxed{\frac{3}{35}}.\]